We are concerned with a numerical method for the optimal control of the reflection directions of a reflected diffusion process, and with either a discounted or an ergodic cost criterion. The Markov chain approximation method is adapted to this nonclassical problem and convergence of the method is proved. The problem originally arose in the important application of rerouting in large trunk-line communications systems. A reasonable heavy-traffic approximation leads to the described model. The numerical method has been applied with success, but no proofs of convergence were given previously. Nonboundary controls can be easily added.